Quantitative Methods: An Introduction for Business Management

10

Simple Linear Regression

In this chapter we take advantage of all the probabilistic and statistical knowledge we have built in the previous chapters to get into the realm of empirical model building. Models come in many forms, but what we want to do here is finding a relationship between two variables, say, x and y, based on a set of n joint observations (x_i, y_i), i = 1,…,n. We got acquainted with correlation in Chapter 8, and if two variables are correlated we can try to put such knowledge to good use for decision making and forecasting. The first step in building a model is choosing a functional form representing the link between the variables of interest. The simplest relationship that comes to mind is linear:

This is called a simple linear regression model. It is obviously linear, but one could and should wonder whether a more complicated, nonlinear functional form is better suited to our task. It is simple since there is only one variable x that we use to “explain” the variable y; multiple linear regression models rely on possibly several explanatory variables. We cover these more advanced models in Chapter 16, since they rely on a definitely more challenging technical machinery. Yet, even the innocent-looking simple linear regression model hides a lot of issues, which are best understood in a simple setting. A deep understanding of these issues is needed to tackle nonlinear ...